Ground penetrating radar (GPR) is a technique whereby electromagnetic signals are transmitted through a material to detect variability or changes within the material. (Annan, A. P., Davis, J. L., Ground Penetrating Radar--Coming of Age at Last; 199; Proceedings of the Fourth Decennial International Conference on Mineral Exploration (Exploration '97), Toronto, Canada, Sep. 14 to Sep. 18, 1997).
The objective is to create an ultra-wide band electromagnetic signal generation source which has controlled or predictable directionality, polarization and bandwidth. In most practical implementations, an electric dipole or variation on this type of antenna is normally used. The advantage of a relatively short electric dipole is that it has controlled directivity and polarization characteristics across the whole spectral bandwidth that can be energized. (Samaddar, S. N. and Mohole, E. L., Some Basic Properties of Antennas Associated with Ultra Wide-band Radiation: Ultra wideband, Short-Pulse Electromagnetics, 1997; 3, Baum et al, Plennum Press, New York, p. 147). Unlike conventional communications antenna needs, where tuned resonant antennas are used for efficiency, the GPR and other UWB radar antennas must deliver impulse response fidelity with efficiency being of secondary importance.
A number of names are given to radar systems with very wide bandwidths. Ground penetrating radar is the name applied to ultra-wide band, impulse style, or base-band radar systems that are used to probe into earth materials or man-made construction materials that form buildings, roads or other such structures. In general, these lossy dielectric materials can be penetrated to some depth and the structure inside mapped. To be effective the transducers must generate very wide-band signals so that the features can be resolved. At the same time the polarization and the directivity have to be controllable or invariant. If not, then spatial mixing of polarization will make spatial deconvolution virtually impossible.
A simple dipole antenna source system (prior art as shown in FIG. 1) comprises a voltage source v(t) with a source impedance defined as which drives the feed point that is in the centre of a piece of wire. Currents flow along the thin wire, causing the emission of an electromagnetic field. (Samaddar, S. N. and Mohole, E. L., supra; Franceshetti, G. and Papas, C. H., Pulsed Antennas; 1974; IEEE Trans, AP. 22, p. 651). The electromagnetic wave field is the source of signals which are used to probe in the materials or applications described herein.
While depicted as a straight line, the dipole in some applications can be three-dimensional and, for example form a V with its vertex at the feed point. For the purposes of understanding electrical current flow, the antenna can be approximated to a first order by a parallel wire transmission line (prior art, as shown in FIG. 2). A parallel wire transmission line is the equivalent of the antenna arms for all intents and purposes. When such an approximation is made, the parallel wire transmission line has a characteristic impedance. ##EQU1## where Z.sub.o is the host material electromagnetic impedance, and ##EQU2## where h is the antenna arm length and a is the wire diameter, and .OMEGA. is the geometric factor for the thin wire antenna arm impedance. The above approximation holds when the value of .OMEGA. is much greater than 1.
When the dipole antenna is mathematically approximated by the parallel wire transmission line, the termination at the end of the transmission line (which is called the load), Z.sub.L, is very large. For all intents and purposes EQU Z.sub.L .apprxeq..infin.,
For GPR applications, the goal is to create an emitted electric field, which has a time variation, which is a close replica of the excitation voltage v(t). If Z.sub.S is equal to Z.sub.A and Z.sub.L =.infin., a short time duration transient voltage v(t) will create a current v(t)/Z.sub.A which travels down the antenna arm, is reflected back to the source and absorbed into the source impedance. The current travels along the antenna arms (or transmission line) at velocity c, for the material hosting the antenna arms. The transit time for the current along the antenna arm and back to the source at the feed is ##EQU3##
Optimal performance is achieved when Z.sub.S is matched to Z.sub.A. Unfortunately, achieving such a match is difficult to near impossible since Z.sub.A can be affected by changes in the surroundings when used in most applications. If Z.sub.S does not match Z.sub.A then all of the current is not absorbed back into the source and multiple reverberations of the current travel up and down the antenna arms dying out in time but re-radiating continually as they bounce back and forth.
FIG. 3 shows the general geometry of the antenna and the electric field at a distance from the dipole. Normally the dipole is usually considered small compared to the distance of the observation point away from the antenna. The electric field at a distance takes the form ##EQU4## The temporal variation of the electric field is composed of several replicas of the excitation voltage. Depending on the duration of the excitation voltage and the antenna arm length, these events or replicas may overlap in time. The result is a smeared and rather complicated waveform. If the antenna arms could be made very long (i.e., let h.fwdarw..infin.), then ##EQU5## Unfortunately this compromise is not practical in many applications and optimizing the performance of finite length of antennas is a critical subject.
As a further complication, if the source impedance and the antenna impedance Z.sub.S and Z.sub.A do not match, then the expression in Equation 3 will have addition terms representing additional radiation events from current which repeatedly bounces back and forth along the antenna arms. Again, an infinite series of terms is possible (Franceshetti, G. and Papas, C. H., Pulsed Antennas; 1974; IEEE Trans, AP. 22, p. 651).
Equation (3) will contain additional terms beyond the ones expressed here which are additional replicas of the excitation voltage created by radiation from discontinuities in the antenna. Numerous attempts have been made to emulate or achieve the result of h.fwdarw..infin. by adding loading to the antenna's arms or otherwise deforming the antennas into a different shape to try to make the current on the arm disappear. (Broome, N. L., Improvements to Non-numerical Methods for Calculating the Transient Behaviour of Linear and Aperture Antennas; 1979; IEEE Trans. Antennas Propagation, AP. 27, p. 51; Wu, T. T. and King, R. W. P., The Cylindrical Antenna with non-reflecting Resistive Loading; 1965; IEEE Trans Antennas Propation, AP. 13, p. 369); Shen, L. C. and Wu, T. T., Cylindrical Antenna with Tapered Resistive Loading; 1967; Radio Science 2, (pg.191).
Another approach to reducing multiple bounces of current along the arms is to minimize reflections from the ends of the antenna arms by effectively making Z.sub.A and Z.sub.L equal. In other words the load on the end of the antenna arms is matched to the impedance of the antenna arms and hence, the currents are absorbed at the ends of the antenna arms and vanish rather than being reflected back into the source. Should this type of matching be achieved, then the radiated field takes a slightly different form. ##EQU6##
In other words, the electric field is reduced from 4 to 3 time-delayed replicas of the excitation voltage. In addition to somewhat simplifying the radiated electric field shape versus time, this approach also reduces the dependency of making the source impedance match the antenna arm impedance. Anything, which will reduce the reverberation of the antenna currents on the arms, is of positive benefit in the battle to achieve wide bandwidth performance from a dipole antenna.